14,629 research outputs found
The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential
As a continuation of our series works on the Boltzmann equation without
angular cutoff assumption, in this part, the global existence of solution to
the Cauchy problem in the whole space is proved in some suitable weighted
Sobolev spaces for hard potential when the solution is a small perturbation of
a global equilibrium
A control on quantum fluctuations in 2+1 dimensions
A functional method is discussed, where the quantum fluctuations of a theory
are controlled by a mass parameter and the evolution of the theory with this
parameter is connected to its renormalization. It is found, in the framework of
the gradient expansion, that the coupling constant of a N=1 Wess-Zumino theory
in 2+1 dimensions does not get quantum corrections.Comment: Comments adde
Aspects of Duality in Nodal Liquids
Starting from a microscopic t-J like model and a SU(2) spin-charge separation
ansatz, a relativistic continuum gauge lagrangian is obtained in the vicinity
of a nodal point of the Fermi surface. The excitations in the pseudogap phase
are described by topological excitations in the dual model which has a Z_2
global symmetry due to the effect of instantons. Confinement of spinon and
holons emerge from this picture. The adjoint and fundamental strings are
associated with stripes. As the spin gap decreases a local Z_2 symmetry
emerges.Comment: 15 pages revtex, no figure
Global existence and full regularity of the Boltzmann equation without angular cutoff
We prove the global existence and uniqueness of classical solutions around an
equilibrium to the Boltzmann equation without angular cutoff in some Sobolev
spaces. In addition, the solutions thus obtained are shown to be non-negative
and in all variables for any positive time. In this paper, we study
the Maxwellian molecule type collision operator with mild singularity. One of
the key observations is the introduction of a new important norm related to the
singular behavior of the cross section in the collision operator. This norm
captures the essential properties of the singularity and yields precisely the
dissipation of the linearized collision operator through the celebrated
H-theorem
Regularizing effect and local existence for non-cutoff Boltzmann equation
The Boltzmann equation without Grad's angular cutoff assumption is believed
to have regularizing effect on the solution because of the non-integrable
angular singularity of the cross-section. However, even though so far this has
been justified satisfactorily for the spatially homogeneous Boltzmann equation,
it is still basically unsolved for the spatially inhomogeneous Boltzmann
equation. In this paper, by sharpening the coercivity and upper bound estimates
for the collision operator, establishing the hypo-ellipticity of the Boltzmann
operator based on a generalized version of the uncertainty principle, and
analyzing the commutators between the collision operator and some weighted
pseudo differential operators, we prove the regularizing effect in all (time,
space and velocity) variables on solutions when some mild regularity is imposed
on these solutions. For completeness, we also show that when the initial data
has this mild regularity and Maxwellian type decay in velocity variable, there
exists a unique local solution with the same regularity, so that this solution
enjoys the regularity for positive time
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Oxygen isotope ratios of large cosmic spherules: Carbonaceous and ordinary chondrite parent bodies
Tunable coupling of superconducting qubits
We study an LC-circuit implemented using a current-biased Josephson junction
(CBJJ) as a tunable coupler for superconducting qubits. By modulating the bias
current, the junction can be tuned in and out of resonance and entangled with
the qubits coupled to it. One can thus implement two-qubit operations by
mediating entanglement. We consider the examples of CBJJ and charge--phase
qubits. A simple recoupling scheme leads to a generalization to arbitrary qubit
designs.Comment: To appear in Phys. Rev. Lett., 3 figure
QED in external fields, a functional point of view
A functional partial differential equation is set for the proper graphs
generating functional of QED in external electromagnetic fields. This equation
leads to the evolution of the proper graphs with the external field amplitude
and the external field gauge dependence of the complete fermion propagator and
vertex is derived non-perturbativally.Comment: 8 pages, published versio
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